What is 8*2\div 3\div 6\div 8-6\div 5*4\div 3 ?

The solution to 8*2\div 3\div 6\div 8-6\div 5*4\div 3 is -67/45

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Popular >

82\div 3\div 6\div 8-6\div 54\div 3

Solution

8 \cdot 2 \div 3 \div 6 \div 8 - 6 \div 5 \cdot 4 \div 3

Solution

- \frac{67}{45}

Solution steps

8 \cdot 2 \div 3 \div 6 \div 8 - 6 \div 5 \cdot 4 \div 3

Follow the PEMDAS order of operations

Multiply and divide (left to right)

8 \cdot 2 \div 3 \div 6 \div 8 : \frac{1}{9}

8 \cdot 2 \div 3 \div 6 \div 8

8 \cdot 2 = 16

= 16 \div 3 \div 6 \div 8

16 \div 3 = \frac{16}{3}

= \frac{16}{3} \div 6 \div 8

\frac{16}{3} \div 6 = \frac{8}{9}

\frac{16}{3} \div 6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{16}{3} \div \frac{6}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{16}{3} \cdot \frac{1}{6}

Cross-cancel common factor:

2

16, 6

Greatest Common Divisor (GCD)

Prime factorization of

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

The prime factors common to

16, 6

are

= 2

= \frac{8}{3} \cdot \frac{1}{3}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{8 \cdot 1}{3 \cdot 3}

Multiply the numbers:

8 \cdot 1 = 8

= \frac{8}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{8}{9}

= \frac{8}{9} \div 8

\frac{8}{9} \div 8 = \frac{1}{9}

\frac{8}{9} \div 8

Convert element to fraction:

8 = \frac{8}{1}

= \frac{8}{9} \div \frac{8}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{8}{9} \cdot \frac{1}{8}

Cross-cancel:

8

= \frac{1}{9}

= \frac{1}{9}

= \frac{1}{9} - 6 \div 5 \cdot 4 \div 3

Multiply and divide (left to right)

6 \div 5 \cdot 4 \div 3 : \frac{8}{5}

6 \div 5 \cdot 4 \div 3

6 \div 5 = \frac{6}{5}

= \frac{6}{5} \cdot 4 \div 3

\frac{6}{5} \cdot 4 = \frac{24}{5}

\frac{6}{5} \cdot 4

Convert element to fraction:

4 = \frac{4}{1}

= \frac{6}{5} \cdot \frac{4}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{6 \cdot 4}{5 \cdot 1}

Multiply the numbers:

6 \cdot 4 = 24

= \frac{24}{5 \cdot 1}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{24}{5}

= \frac{24}{5} \div 3

\frac{24}{5} \div 3 = \frac{8}{5}

\frac{24}{5} \div 3

Convert element to fraction:

3 = \frac{3}{1}

= \frac{24}{5} \div \frac{3}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{24}{5} \cdot \frac{1}{3}

Cross-cancel common factor:

3

= \frac{8}{5}

= \frac{8}{5}

= \frac{1}{9} - \frac{8}{5}

Add and subtract (left to right)

\frac{1}{9} - \frac{8}{5} : - \frac{67}{45}

\frac{1}{9} - \frac{8}{5}

\frac{1}{9} - \frac{8}{5} = - \frac{67}{45}

\frac{1}{9} - \frac{8}{5}

Least Common Multiplier of

9, 5 : 45

9, 5

Least Common Multiplier (LCM)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Multiply each factor the greatest number of times it occurs in either

9

5

= 3 \cdot 3 \cdot 5

Multiply the numbers:

3 \cdot 3 \cdot 5 = 45

= 45

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

45

For

\frac{1}{9} :

multiply the denominator and numerator by

5

\frac{1}{9} = \frac{1 \cdot 5}{9 \cdot 5} = \frac{5}{45}

For

\frac{8}{5} :

multiply the denominator and numerator by

9

\frac{8}{5} = \frac{8 \cdot 9}{5 \cdot 9} = \frac{72}{45}

= \frac{5}{45} - \frac{72}{45}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5 - 72}{45}

Subtract the numbers:

5 - 72 = - 67

= \frac{- 67}{45}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{67}{45}

= - \frac{67}{45}

= - \frac{67}{45}

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Frequently Asked Questions (FAQ)

What is 8*2\div 3\div 6\div 8-6\div 5*4\div 3 ?
The solution to 8*2\div 3\div 6\div 8-6\div 5*4\div 3 is -67/45